Im having a little trouble grasping a little maths that Cantor came up with.

Its the one where you write every single decimal real number in a list, then you take the first decimal digit of the first number, the second digit of the second number in the list, the third digit of the third number etc. to get a 'new' number.

you then change that number in a set way, and you have a completely new decimal.

 

my problem is that although you have a number that has a different first digit to the first number, so its not the first one, and its not the second one, and so on, you will still have written every possible decimal real number, so how is it not in the list?

 

 

 

That is the point. Proof by contradiction. Assume you can make such a complete list and then show you can't, therefore real numbers are uncountable.